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Frauke Dobnik
Energy Consumption and
Economic Growth Revisited:
Structural Breaks and
Cross-section Dependence
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Ruhr Economic Papers #303
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ISSN 1864-4872 (online) – ISBN 978-3-86788-348-1
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Ruhr Economic Papers #303
Frauke Dobnik
Energy Consumption and
Economic Growth Revisited:
Structural Breaks and
Cross-section Dependence
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ISSN 1864-4872 (online)
ISBN 978-3-86788-348-1
Frauke Dobnik1
Energy Consumption and Economic
Growth Revisited: Structural Breaks and
Cross-section Dependence
Abstract
This paper examines the causal relationship between real GDP and energy consumption
for 23 OECD countries from 1971 to 2009. Using recently developed panel econometric
techniques the present paper takes into account structural breaks and cross-section
dependence when analysing the energy consumption-growth nexus. The empirical
results of this study indicate that there exists a long-run equilibrium relationship
between real GDP and energy consumption, and the impact of real GDP on energy
consumption is larger than vice versa. Furthermore, the empirical evidence of a dynamic
panel error-correction model reveals a bidirectional causal relationship between
economic growth and energy consumption in both the short and long run.
JEL Classification: C33, C23, Q43
Keywords: Energy consumption; panel unit roots and cointegration; structural breaks;
cross-section dependence; panel error-correction model; Granger causality
December 2011
1 Ruhr Graduate School in Economics (RGS Econ) and University of Duisburg-Essen. – I am
grateful to Ansgar Belke, Hashem M. Pesaran, Joscha Beckmann, and Paul Baker for valuable
suggestions and helpful comments. I also would like to thank Josep Lluís Carrion-i-Silvestre, Joakim
Westerlund and Takashi Yamagata for providing the GAUSS codes for their tests and estimators used
in this paper. Financial support provided by the Ruhr Graduate School in Economics is gratefully
acknowledged. – All correspondence to Frauke Dobnik, Ruhr Graduate School in Economics, c/o
University of Duisburg-Essen, Department of Economics, Chair for Macroeconomics, Prof. Dr.
Ansgar Belke, Universitätsstr. 12, 45117 Essen, Germany, E-Mail: [email protected].
1
Introduction
The question of whether or not energy conservation policies affect economic activity has attracted a lot of attention in previous and current research. The direction of causation between
energy consumption and economic growth is of crucial importance in the international debate on global warming and the reduction of greenhouse gas emissions. Furthermore, since
the world’s leading economies agreed on the Kyoto Protocol in 2005 to limit their greenhouse gas emissions relative to the amounts emitted in 1990, the information of this causal
relation has become increasingly important. Hence, the developed countries require a suitable basis of decision-making to formulate sensible energy policies that account for any
affect of reducing energy consumption to lower dioxide emissions on economic growth. For
instance, if causality runs from energy consumption to economic growth, energy conservation policies may have a negative impact on an economy’s growth.
The literature on the energy consumption-GDP growth nexus proposes four testable hypotheses regarding the possible outcomes of causality. The growth hypothesis suggests that
energy consumption is a crucial component in growth, directly or indirectly as a complement to capital and labour as input factors of production. Hence, a decrease in energy
consumption causes a decrease in real GDP. In this case, the economy is called ‘energy dependent’ and energy conservation policies may be implemented with adverse effects on real
GDP. By contrast, the conservation hypothesis claims that policies directed towards lower
energy consumption may have little or no adverse impact on real GDP. This hypothesis is
based on a uni-directional causal relationship running from real GDP to energy consumption. Bi-directional causality corresponds with the feedback hypothesis, which argues that
energy consumption and real GDP affect each other simultaneously. In this case, policy
makers should take into account the feedback effect of real GDP on energy consumption by
implementing regulations to reduce energy use. Finally, the neutrality hypothesis, which is
confirmed by the absence of any causal relation, indicates that reducing energy consumption
does not affect economic growth or vice versa. Hence, energy conservation policies would
not have any impact on real GDP.
4
It should be noted, however, that the exclusive investigation of the direction of causation
between energy consumption and economic growth may not provide unambiguous policy
implications. Energy conservation policies cannot sensibly be constituted without the consideration of economic or environmental factors such as energy supply infrastructure, energy
efficiency considerations or institutional constraints (Mahadevan and Asafu-Adjaye, 2007).
For instance, energy conservation policies that effect a reduction in energy consumption due
to improved energy efficiency may raise the productivity of energy consumption, which in
turn may stimulate economic growth. Thus, a shift from less efficient energy sources to
more efficient and less polluting options may establish a stimulus rather than an obstacle
to economic growth (Costantini and Martini, 2010). Alternatively, poor energy supply infrastructure or other supply side disruptions that decrease energy consumption could indeed
induce an adverse impact on economic growth. Furthermore, high substitutability between
energy and other input factors on the production side can explain possible economic growth
without a considerable increase in energy consumption.
The present study analyses the relationship between energy consumption and GDP of 23
developed countries covering the period from 1971 to 2009. The purpose of this paper is
to overcome several shortcomings of previous and frequently used econometric methods to
intervene convincingly in the discussion about the direction of causation between energy
consumption and economic growth. Until now, most studies have analysed single countries
on the basis of annual data and failed to reach a consensus on this causal relationship. As
for many countries there are only annual data available, the span usually covers no more
than 20-30 years. However, it is well-known that standard time series tests, such as the
augmented Dickey-Fuller unit root test (Dickey and Fuller, 1979) and the Johansen (1991,
1995) cointegration test, have low statistical power, especially when the span of data is short,
(Campbell and Perron, 1991). In response, recent studies have used panel data to extend the
time series dimension by the cross-sectional dimension and, hence, exploit additional information. As panel-based tests rely on a broader information set, the power can substantially
be increased and tests are more accurate and reliable. Studies using panel data, however,
also provide ambiguous results.
5
One reason may be that almost all of them neglect the presence of structural breaks. It is
well-known that inappropriately omitting breaks can lead to misleading inference in time
series testing (Perron, 1989). That is also true for panel tests since panel data also include
the time series dimension as mentioned by Lee and Chiu (2011). The importance of taking
into account structural breaks when analysing energy consumption and GDP can be confirmed by several past events. First of all, the first oil crisis in 1973 occurred when the
Arab oil embargo was proclaimed. The Iranian revolution followed in 1978, accompanied
by exploding oil prices and a period of high inflation during the late 1970s. Furthermore,
the global economic recession in the early 1980s may represent a potential structural break.
Further critical events are: The 1986s oil glut caused by decreasing demand following the
1970s energy crisis, the stock market crash in the United States in 1987, the periods of moderate economic growth and low inflation in Western industrialised countries in the late 1980s
and early 1990s, the oil price increase after Iraq’s invasion of Kuwait 1990, and, finally, the
1997-1999 Asian financial crisis. Since all those mentioned events occurred within the period covered in this analysis, the consideration of structural breaks is strongly advisable.
Hence, the present study makes a substantial contribution to the existing literature by doing
so in a panel framework.
A second explanation for the failure to reach a consensus on the direction of causation between energy consumption and economic growth may be the neglect of dependence across
the countries in a panel by using first generation panel unit root and cointegration tests.
First generation panel tests are characterised by the assumption of independent cross-section
members. This condition is unrealistic in view of the strong inter-economy linkages and
therefore, is likely to be violated often, for instance, because of common oil price shocks.
But most existing residual based tests use the assumption of cross-sectional independence
to be able to get a convenient asymptotic distribution for the test statistic. The independence
of the cross-section members allows for the use of standard asymptotic tools, such as the
Central Limit Theorem. However, Banerjee et al. (2004) showed by means of simulations
experiments that inappropriately assuming cross-sectional independence in the presence of
cross-member cointegration can have distortionary impacts on the panel inference. Thus,
6
they argued that the conclusions of many empirical studies may be based upon misleading
inference since the assumption of independent panel members is usually not valid (Urbain
and Westerlund, 2006). Until recently, only few so-called second generation panel tests have
been proposed that take into account the existence of cross-sectional dependency relations
(see Breitung and Pesaran, 2008, for a recent survey). Hence, the innovative contribution
of the present paper is the application of panel econometric techniques that consider both
structural breaks and cross-sectional dependence to provide more accurate and reliable results.
The remainder of this paper is organised as follows. Section 2 reviews the literature related
to the causal relationship between energy consumption and economic growth using panel
data. Given that the panel econometric methods applied in the present study are recently
developed and less used in the empirical literature, Section 3 provides additional details on
these methods. The data is presented and analysed in Section 4, which reveals the empirical
results. Finally, Section 5 provides conclusions and policy implications.
2
Literature review
The relationship between energy consumption and economic growth is a widely studied research topic, however, the empirical evidence is mixed and conflicting with respect to the
direction of causation. In addition to the methodical weaknesses described in the Introduction, this discrepancy in results may also be due to country-specific heterogeneity in climate
conditions, economic development and energy consumption patterns. The vast literature on
single country analysis using time series econometrics draws on the initial work of Kraft
and Kraft (1978). This study provides evidence in favour of causality running from income
to energy consumption in the United States for the period 1947-1974. In recent years researchers have taken advantage of newly developed panel econometric techniques. Table
1 summarises the thereby existing panel data studies on the energy consumption-growth
7
nexus.1 Furthermore, there are also some panel data studies on the relationship between
growth and specific components of total energy consumption such as coal (Apergis and
Payne, 2010a,b), electricity (e.g., Acaravci and Ozturk, 2010; Apergis and Payne, 2011a;
Chen et al., 2007; Narayan and Smyth, 2009), nuclear energy (Apergis and Payne, 2010d;
Lee and Chiu, 2011), and renewable energy (see, e.g., Apergis and Payne, 2010e; Sadorsky,
2009).
Table 1: Overview of panel data studies on the energy consumption-economic growth nexus
Authors
Period
Countries
Causality
Lee (2005)
Al-Iriani (2006)
Lee and Chang (2007)
1975-2001
1971-2002
1965-2002
1971-2002
1971-2002
18 developing countries
GCC countries
22 developed countries
18 developing countries
10 net energy exporters 10
10 net energy importers
11 oil exporting countries
26 high income countries
15 upper middle income countries
22 lower middle income countries
19 low income countries
22 OECD countries
16 Asian countries
G-7 countries
11 countries within the
Commonwealth of Independent States
6 Central American countries
9 Pacific Island countries
88 countries
9 South American countries
26 OECD countries
45 non-OECD countries
25 OECD countries
13 upper middle income countries
24 lower middle income countries
14 low income countries
80 countries
25 OECD countries
40 Sub-Saharan African countries
4 developed Asia-Pacific countries
4 developing Asia-Pacific countries
Energy Growth
Growth Energy
Energy ↔ Growth
Growth Energy
Growth Energy
Energy Growth
Growth Energy
Growth Energy
Growth Energy
Growth Energy
Energy ¬ Growth
Energy ↔ Growth
Energy Growth
Energy Growth
Mahadevan and
Asafu-Adjaye (2007)
Mehrara (2007)
Huang et al. (2008)
1971-2002
1971-2002
Lee et al. (2008)
Lee and Chang (2008)
Narayan and Smyth (2008)
Apergis and Payne (2009a)
1960-2001
1971-2002
1972-2002
1991-2005
Apergis and Payne (2009b)
Mishra et al. (2009)
Sinha (2009)
Apergis and Payne (2010c)
Costantini and Martini (2010)
Lee and Lee (2010)
Ozturk et al. (2010)
1980-2004
1980-2005
1975-2003
1980-2005
1960-2005
1970-2005
1978-2004
1971-2005
Apergis and Payne (2011b)
Belke et al. (2011)
Kahsai et al. (2011)
Niu et al. (2011)
1990-2007
1981-2007
1980-2007
1971-2005
Energy ↔ Growth
Energy Growth
Energy ↔ Growth
Energy ↔ Growth
Energy Growth
Energy ↔ Growth
Energy ↔ Growth
Energy ↔ Growth
Energy ↔ Growth
Energy ↔ Growth
Growth Energy
Energy ↔ Growth
Energy ↔ Growth
Energy ↔ Growth
Energy ↔ Growth
Growth Energy
Notes: X Y means variable X Granger-causes variable Y. X ¬ Y means that there no Granger-causality exists.
The first panel data study on the relationship between energy consumption and growth by
1
For a detailed literature overview including time series studies on the causal relationship between energy
consumption and economic growth, see the recent surveys by Ozturk (2010) and Payne (2010)
8
Lee (2005) examined 18 developing countries over the period 1975-2001. He found unidirectional causality running from energy consumption to growth. This finding suggests
that energy conservation may harm economic growth in developing countries. In contrast,
Al-Iriani (2006) found uni-directional causality running from growth to energy consumption for six member countries of the Gulf Cooperation Council (GCC) covering the period
1971-2002. Thus, energy conservation policies may be adopted by the GCC without any
adverse effects on economic growth. Correspondingly, the panel data studies listed in Table
1 in general provide ambiguous empirical results on the energy consumption-growth nexus
similar to that found in time series studies. Even the distinction between developed and
developing countries leads to no clear evidence for either group of countries. Similar to
Lee (2005) and Al-Iriani (2006), most panel data analyses have applied the panel unit root
tests proposed by Hadri (2000), Levin et al. (2002) (LLC) and/or Im et al. (2003) (IPS), the
Pedroni (1999, 2004) panel cointegration test and the panel generalised method of moments
(GMM) estimator proposed by Arellano and Bond (1991) to test for panel Granger causality.
Furthermore, the listed studies also often use the Breitung (2000), and the Fisher-type ADF
and PP tests (see Choi, 2001; Maddala and Wu, 1999) to test for unit roots. In addition, the
long-run relationship between energy consumption and GDP, which is commonly confirmed
by means of the already mentioned Pedroni (1999, 2004) test, is almost always estimated
with fully modified OLS (FMOLS) as suggested in Pedroni (2000). In view of the repeated
application of the same methods that continue to provide conflicting evidence, even for panels of similar countries, further methodological improvements seem to be necessary.
One reasonable issue is the consideration of structural breaks as illustrated in the Introduction. Another important point to note is that all panel unit root and cointegration tests mentioned above are so-called first generation panel tests, meaning that they restrictively assume
independence across panel members. However, there are only a few panel data studies that
apply appropriate methods to tackle these issues. Firstly, Chen and Lee (2007) re-investigate
the stationarity of energy consumption per capita for seven regional panel sets covering the
1971-2002 period in the presence of potential structural breaks. Consequently, they used
the panel unit root test proposed by Carrion-i-Silvestre et al. (2005) (CBL) which allows
9
for multiple level shifts including bootstrap methods to consider general forms of crosssectional dependence as well. Their results suggest evidence in favour of stationary energy
consumption. Narayan and Smyth (2008) also applied the CBL test to the G-7 countries
over the period 1972 to 2002, but without a structural break. However, they used the panel
cointegration technique with multiple structural breaks of Westerlund (2006). Their main
finding is that the Pedroni (1999) cointegration test failed to find evidence for a long-run
relationship whereas cointegration can be detected when structural breaks are incorporated.
As a robustness check of their stationarity results, Costantini and Martini (2010) performed
the LM panel unit root test proposed by Im et al. (2005) which considers the presence of a
single break. The evidence in favour of non-stationarity mostly remains the same. A study
which does not account for structural breaks but cross-section dependence resulting from
unobserved common factors is proposed by Belke et al. (2011). They applied the Bai and
Ng (2004) PANIC procedure and the cointegration test approach suggested by Gengenbach
et al. (2006) to test idiosyncratic and common components separately for unit roots and
cointegration relations.
Moreover, there are no further panel data studies on the relationship between total energy
consumption and growth dealing with structural breaks and/or cross-sectional dependence.
However, in the analysis of the relation between electricity consumption and GDP of six
Middle Eastern countries for the sample 1974-2002, Narayan and Smyth (2009) applied
once again the Westerlund (2006) test to take into account structural breaks. Apergis and
Payne (2010b) examined the integration property of coal consumption of 25 OECD countries over the period 1980-2005 by means of several panel unit root tests with structural
breaks: Carrion-i-Silvestre et al. (2005), Im et al. (2005), and Westerlund (2005). The latter
test examines the case in which multiple endogenous breaks are allowed in the level of the
series. The empirical results suggest, even in the presence of structural breaks, integration of
order one for coal consumption. Furthermore, they applied the Larsson et al. (2001) panel
coinetgration test (LLL) that allows for cross-sectional dependence through the effects of
the dynamics of the short run. Finally, Lee and Chiu (2011) analysed nuclear energy consumption over the period 1971 to 2006 for six developed countries also using Westerlund
10
(2006)’s panel cointegration test. In their study the corresponding estimated break dates are
presented but not the results referring to the existence of cointegration.
Even though all these studies provide evidence in favour of the presence of a single or multiple structural breaks none of them consequently consider that issue in both the unit root
and cointegration tests. Furthermore, except for the CBL test and the cointegration test
approach of Gengenbach et al. (2006), all applied methods on total energy consumption neglect the existence of dependence across panel members. Consequently, this study take into
account both structural breaks and cross-section dependence when testing for unit roots and
cointegration, respectively.
3
Methodology
Since the pioneering work of Perron (1989) it is well known that it is critical to allow for
structural breaks when testing time series for unit roots. The failure to take into account
the potential presence of structural breaks may lead to misleading inference regarding the
order of integration. For instance, a stationary time series with a broken trend could be
mistaken for a non-stationary process if the unit root test neglects the presence of structural
breaks (Perron, 1989). Furthermore, Breitung and Pesaran (2008) proposed that in many
empirical analyses using panel data it is inappropriate to assume that cross-section members
are independent. Indeed, the assumption of independence is usually not valid, in particular
in the analysis of macroeconomic or financial data that have strong inter-economy linkages
(Urbain and Westerlund, 2006).
Consequently, this paper uses recently developed panel techniques that accommodate both
structural breaks and cross-sectional dependence simultaneously rather than neglecting both
or tackling only one of these issues at a time. Since these econometric methods have yet
been rarely applied in the empirical literature, this section discusses the techniques that are
used in this study to analyse the energy consumption-growth nexus. First, the test for crosssectional independence proposed by Pesaran (2004) is briefly presented. Second, this study
describes the panel unit root test developed by Bai and Carrion-i-Silvestre (2009) which
11
allows for structural breaks and cross-sectional dependence. Third, the panel cointegration
test suggested by Westerlund and Edgerton (2008), which also considers structural breaks
and dependence across countries, is introduced. Fourth, Sub-section 3.4 discusses Pesaran
(2006)’s common correlated effects (CCE) estimators that are used to estimate the longrun relationship between energy consumption and GDP. Finally, the pooled mean group
estimator for non-stationary heterogeneous panels suggested by Pesaran et al. (1999) to
establish dynamic panel causality is briefly presented.
3.1
Cross-section dependence
The cross-section dependence (CD) test proposed by Pesaran (2004) tests the null hypothesis of zero dependence across the panel members and is applicable to a variety of panel
data models such as stationary and unit root dynamic heterogeneous panels with structural
breaks, with small T and large N (Pesaran, 2004). The CD test is based upon an average of
all pair-wise correlations of the ordinary least squares (OLS) residuals from the individual
regressions in the panel data model
yit = αi + βi xit + uit ,
(1)
where i = 1, ..., N represents the cross-section member, t = 1, ..., T refers to the time period,
and xit is a (k×1) vector of observed regressors. The intercepts, αi , and the slope coefficients,
βi , are allowed to vary across the panel members.
The CD test statistic is defined as
CD =
⎞
⎛ N−1 N
⎜⎜⎜ ⎟⎟⎟
2T
⎜⎜⎜
ρ̂i j ⎟⎟⎟ → N(0, 1),
N(N − 1) ⎝ i=1 j=i+1 ⎠
(2)
where ρ̂i j is the sample estimate of the pair-wise correlation of the OLS residuals, ûit , associated with Equation (1)
T
ρ̂i j = ρ̂ ji = T
2
t=1 ûit
12
t=1 ûit û jt
1/2 T
t=1
û2jt
1/2 .
(3)
3.2
Panel unit root test
Bai and Carrion-i-Silvestre (2009) developed panel unit root statistics which pool modified
Sargan and Bhargava (1983) (MSB) tests for individual time series, taking into account both
multiple structural breaks and cross-section dependence through a common factors model
proposed by Bai and Ng (2004). They allow for structural breaks in the level, slope or both
at different dates for different countries and may have different magnitudes of shift. Additionally each series can have a different number of breaks and within each series the number
of breaks in the level and the slope can also be different. Hence, the test approach proposed
by Bai and Carrion-i-Silvestre (2009) takes into account a high degree of heterogeneity
across countries. Furthermore, the common factors may be stationary, non-stationary or a
combination of both. The common factor approach allows the common shocks to affect
countries differently via heterogeneous factor loadings. Bai and Carrion-i-Silvestre (2009)
modified the Bai and Ng (2004) PANIC procedure to achieve a robust decomposition into
common and idiosyncratic components in the presence of structural breaks. They developed
an iterative estimation procedure that is appropriate to deal with heterogeneous breaks in the
deterministic components.
In summary, their overall procedure consists of the following steps:
1. Difference the variables and estimate the number and locations of structural breaks
for each time series.
2. Given the locations of the structural breaks, estimate the common factors, factor loadings, and the magnitudes of changes via the iteration procedure mentioned above.
3. Calculate the residuals for each time series based on the estimated quantities in step 2
and then obtain the cumulative sum of residuals as described in Bai and Ng (2004).
4. Determine the modified univariate MSB test for each residual series.2
5. Construct the panel MSB test by pooling the individual ones.
2
The univariate MSB test for unit root was originally introduced by Stock (1999), who generalised the
procedure of Sargan and Bhargava (1983) to non-i.i.d. and non-normal errors.
13
These steps are based on the following general panel data model:
Xi,t = Di,t + Ft πi + ei,t
(4)
(I − L)Ft = C(L)ut
(5)
(1 − ρi L)ei,t = H − i(L)εi,t ,
(6)
where the index i = 1, ..., N represents panel members and t = 1, ..., T denotes the time
period. C(L) = ∞j=0 C j L j and Hi (L) = ∞j=0 Hi, j L j , where L is the lag operator and ρi is the
autoregressive parameter. The component Di,t represents the deterministic part of the model,
Ft is a (r × 1) vector of common factors, and ei,t denotes the idiosyncratic disturbance term.
Despite the operator (1 − L) in Equation 6, Ft need not to be I(1). The integration property
of the Ft depends on the rank of C(1). If C(1) = 0, the Ft is I(0). If C(1) is of full rank, then
each component of Ft is I(1). If C(1) = 0 but not full rank, then some components of Ft are
I(1) and some are I(0).3
With regard to the deterministic component Di,t , Bai and Carrion-i-Silvestre (2009) propose
the following two models:
Model 1:
Di,t = μi +
li
θi, j DUi, j,t
(7)
j=1
Model 2:
Di,t = μi + βi t +
li
j=1
θi, j DUi, j,t +
mi
γi,k DT i,k,t ,
(8)
k=1
where li and mi denote the structural breaks affecting the mean and the trend of a series, respectively, which are not necessarily equal. The dummy variables are defined as DUi, j,t = 1
i
i
i
for t > T a,i j and 0 otherwise, and DT i,k,t = (t − T b,k
) for t > T b,k
and 0 otherwise. T a,i j and T b,k
represent the jth and kth dates of the breaks in the level and trend, respectively, for the ith
individual with j = 1, ..., li and k = 1, ..., mi .
The introduced common factors capture the co-movement of the time series as well as crosssection correlation. Since those factors are unobserved, they need to be consistently estimated. Following Bai and Ng (2004), Bai and Carrion-i-Silvestre (2009) estimate these un3
For a detailed description of the underlying set of assumptions, see Bai and Carrion-i-Silvestre (2009)
14
observed common factors by applying the principal components analysis to the differenceddetrended model. They provide separate analyses for the two deterministic models as the
limiting distribution of the MSB statistic depends on the specification.4
Bai and Carrion-i-Silvestre (2009) pool the individual MSB test statistics to increase the
statistical power. The standard approach to pooling described in Levin et al. (2002) requires
cross-sectionally independent panel members, a condition that is not fulfilled in this framework. However, the combination of individual MSB test statistics is appropriate since the
ei,t are independent across the panel units. This follows from the fact that the limiting distributions are free from the common factors. Bai and Carrion-i-Silvestre (2009) provide
two approaches for pooling the individual test statistics so as to test the null hypothesis H0 :
ρi = 1 for all i = 1, ..., N against the alternative H1 : |ρi | < 1 for some i. The first approach is
to use the average of individual statistics:
Z=
with MSB(λ) = N −1
N
i=1
√ MSB(λ) − ξ̄
N
→ N(0, 1),
ζ̄
MSBi (λi ), ξ̄ = N −1
N
i=1 ξi ,
and ζ 2 = N −1
(9)
N
2
i=1 ζi ,
where ξi and ζi2
denote the mean and the variance of the individual modified MSBi (λi ) statistic, respectively,
and λi = T ib /T represents the break fraction parameter.5 The individual MSB statistics are
asymptotically invariant to mean breaks, but not to breaks in the linear trend. Hence, Bai and
Carrion-i-Silvestre (2009) introduced a second approach based on simplified test statistics
which are invariant to both mean and trend breaks:
Z∗ =
with MSB∗ (λ) = N −1
N
i=1
√ MSB∗ (λ) − ξ¯∗
N
→ N(0, 1),
ζ¯∗
(10)
N ∗
N ∗2
MSB∗i (λi ), ξ¯∗ = N −1 i=1
ξi , and ζ ∗2 = N −1 i=1
ζi , where ξi∗
and ζi∗2 denote the mean and the variance of the individual modified MSB∗i (λi ) statistic,
respectively, and λi = T ib /T represents the break fraction parameter.6
4
See Bai and Carrion-i-Silvestre (2009) for details.
See Bai and Carrion-i-Silvestre (2009) for a description of the individual MSB statistics.
6
See Bai and Carrion-i-Silvestre (2009) for a description of the individual simplified MSB statistics.
5
15
To yield satisfactory results when pooling, Bai and Carrion-i-Silvestre (2009) consider the
second approach proposed by Maddala and Wu (1999) and Choi (2001) that pools the pvalues of the individual tests:
P = −2
Pm =
N
ln pi → χ22N
i=1
N
−2 i=1
ln pi − 2N
→ N(0, 1),
√
4N
(11)
(12)
where pi , i = 1, ..., N, is the individual p-value. Bai and Carrion-i-Silvestre (2009) denote
the corresponding P and Pm statistic that are computed by means of the p-values of the
simplified MSB statistic as P∗ and P∗m , respectively.
3.3
Panel cointegration test
A panel cointegration test that considers both structural breaks and cross-section dependence was developed by Westerlund and Edgerton (2008). Apart from cross-sectional dependence and unknown structural breaks in both the intercept and slope, their test allows
for heteroskedastic and serially correlated errors, as well as cross unit-specific time trends.
Moreover, the structural breaks may be located at different dates for different panel members. Westerlund and Edgerton (2008) propose two versions to test for the null hypothesis
of no cointegration which can be used under those general conditions. Their test is derived
from the Lagrange multiplier (LM)-based unit-root tests developed by Schmidt and Phillips
(1992), Ahn (1993), and Amsler and Lee (1995). The model under consideration is
yit = αi + ηi t + δi Dit + xit βi + (Dit xit ) γi + zit ,
(13)
xit = xit−1 + wit ,
(14)
where the indices i = 1, ..., N and t = 1, ..., T denote panel members and the time period,
respectively. The k-dimensional vector xit contains the regressors and is specified as a random walk. The variable Dit is a scalar break dummy such that Dit = 1 if t > T i and zero
otherwise. Hence, αi and βi represent the cross unit-specific intercept and slope coefficient
16
before the break, while δi and γi represent the change in these parameters after the break. wit
is an error term with mean zero and independent across i.7 The disturbance term zit is generated by the following model that allows cross-sectional dependence through unobserved
common factors
zit = λi Ft + υit
where φi (L) 1 −
pi
j=1
(15)
F jt = ρ j F jt−1 + u jt
(16)
φi (L)Δυit = φi υit−1 + eit ,
(17)
φi j L j is a scalar polynomial in the lag operator L, Ft is a r-
dimensional vector of unobservable common factors F jt with j = 1, ..., r, and λi is the
corresponding vector of factor loading parameters. The error term ut is independent of eit
and wit for all i and t, and eit is mean zero and independent across both i and t. Under the
assumption that ρ j < 1 for all j, it is assured that Ft is stationary involving that the order of
integration of the composite regression error zit depends only on the degree of integration
of the idiosyncratic disturbance term υit . Hence, the relationship in Equation (13) is cointegrated if φi < 0 and spurious if φi = 0.8
Westerlund and Edgerton (2008) test the null hypothesis that all N cross-section units are
spurious (H0 : N1 = 0 with N0 N−N1 ) against the alternative that the first N1 cross-section
units are cointegrated while the remaining N0 N − N1 units are spurious (H1 : N1 > 0).9
For testing purposes the LM principle is used that the score vector has zero mean when
evaluated at the vector of true parameters under the null. Westerlund and Edgerton (2008)
therefore consider the following pooled log-likelihood function
⎛
⎞
N
T
1 2 ⎟⎟⎟⎟
1 ⎜⎜⎜⎜
2
e ⎟.
log(L) = constant −
⎜T log(σi ) − 2
2 i=1 ⎝
σi t=1 it ⎠
7
(18)
For notational simplicity, the model is restricted to allow for only one break.
Further assumptions that are made to develop the test can be found in Westerlund and Edgerton (2008).
Westerlund and Edgerton (2008) argue that the assumption that the cointegrated units lie first is only for
notational simplicity, and is by no means restrictive.
8
9
17
Their test can be derived by first concentrating the log-likelihood function with respect to
σ2i and then evaluating the resulting score at the restricted maximum likelihood estimates.
Let σ̂2i 1/T Tt=1 e2it , then the score contribution for unit i is given by
T
∂ log L
1 = 2
(ΔŜ it − ΔŜ i )(Ŝ it − Ŝ i ),
∂φi
σ̂i t=2
(19)
where Ŝ it is a certain residual defined below, while ΔŜ i and Ŝ i are the mean values of ΔŜ it
and Ŝ it , respectively. The score vector is proportional to the numerator of the least squares
estimate of φi in the regression
ΔŜ it = constant + φi Ŝ it−1 + error.
(20)
It follows that a test of the null of no cointegration for cross-section unit i can be formulated
equivalently as a zero-slope restriction in Equation (20), which can be tested by means of
either the least squares estimate of φi or its t-ratio. Hence, by considering the form of the
log-likelihood function, a panel test of H0 vs. H1 can be constructed by using the crosssectional sum of these statistics for each i.
In the presence of cross-sectional dependence, the variable Ŝ it can be computed as
Ŝ it yit − α̂it − η̂i t − δ̂i Dit − xit β̂i − (Dit xit ) γ̂i − λ̂i F̂t ,
(21)
where the common factor F̂t is the accumulated sum of the principal component estimates
ΔF̂ of ΔF. This defactoring makes the test robust to cross-sectional dependence generated
by common factors, while the test regression can additionally be augmented to also make it
robust to serial correlation
ΔŜ it = constant + φi Ŝ it−1 +
pi
j=1
18
φi j ΔŜ it− j + error.
(22)
To obtain the new panel test, Westerlund and Edgerton (2008) define
LMφ (i) T φ̂i
ω̂i
,
σ̂i
(23)
where φ̂i is the least squares estimate of φi in Equation (22) with σ̂i as the estimated standard
error from the same regression, and ω̂2i is the estimated long-run variance of Δυit based on
Ŝ it . To obtain the second test statistic, Westerlund and Edgerton (2008) introduce the t-ratio
of φ̂i given by
LMτ (i) φ̂i
,
SE(φ̂i )
(24)
where SE(φ̂i ) is the estimated standard error of φ̂i . Based on LMφ (i) and LMτ (i) Westerlund and Edgerton (2008) propose the two panel LM-based test statistics for the null of no
cointegration as
LMφ (N) N
1
LMφ (i),
N i=1
and LMτ (N) N
1
LMτ (i).
N i=1
(25)
Finally, in consideration of the asymptotic properties of LMφ (i) and LMτ (i), Westerlund and
Edgerton (2008) obtain the following normalised test statistics10
Zφ (N) =
Zτ (N) =
3.3.1
√
√
N(LMφ (N) − E(Bφ )),
(26)
N(LMτ (N) − E(Bτ )).
(27)
Estimation of breaks
Westerlund and Edgerton (2008) follow the strategy of Bai and Perron (1998) to determine
the location of structural breaks. The approach developed by Bai and Perron (1998) allows
for general forms of serial correlation and heteroskedasticity in the errors, lagged dependent
variables, trending regressors, as well as different distributions for the errors and the regressors across the segments that are separated by the breaks. Moreover, they consider the case
of a partial structural change model meaning that not all parameters are necessarily subject
10
The complete analysis of the asymptotic properties of the newly developed tests and the explicit derivation
of Zφ (N) and Zτ (N) are explained in Westerlund and Edgerton (2008).
19
to shifts. In line with this approach Westerlund and Edgerton (2008) individually estimate
the break point(s) for each panel member i by minimising the sum of squared residuals from
the regression in Equation 13 in first differences. The break point estimator is defined as
1 (Δẑit )2 .
T − 1 t=2
T
τ̂i = arg min
0<τi <1
3.4
(28)
Long-run estimators
Pesaran (2006) proposed common correlated effects (CCE) estimators to estimate heterogeneous panel data models with a multifactor error structure. The basic idea is to filter
the cross-unit specific regressors by means of cross-section averages of the dependent variable and the observed regressors. Thus, cross-sectional dependence can be eliminated since
the unobserved common factors can be well approximated by those cross-section averages.
Therefore, the number of the stationary factors need not to be estimated. The CCE procedure can be computed by running standard panel regressions where the observed regressors
are augmented with cross-sectional averages of the dependent variable and the cross unitspecific regressors. Pesaran (2006) developed two CCE estimators, the pooled and mean
group CCE estimator, to consider two different but related estimation and inference problems: one that concerns the coefficients of the cross unit-specific regressors and the other
that focuses on the means of the individual coefficients. Kapetanios et al. (2011) extend
the work of Pesaran (2006) to the case where the unobserved common factors are nonstationary. They show that the CCE estimators are consistent even in the presence of unit
roots in the unobserved common factors and are also robust to structural breaks in the mean
of those unobserved factors.
Pesaran (2006) assumed the heterogeneous panel data model with yit as the observation on
the i-th panel member at time t for i = 1, ..., N and t = 1, ..., T
yit = αi dt + βi xit + eit ,
20
(29)
where dt represents a (n × 1) vector of observed common effects including, on the one hand,
deterministic components such as intercepts or seasonal dummies and, on the other hand,
non-stationary observed common effects such as the oil price. The observed cross unitspecific regressors are denoted by the (k × 1) vector xit , while the error term eit is specified
by a multifactor structure
eit = γi ft + εit ,
(30)
where ft denotes the (m × 1) vector of unobserved common factors and εit are the cross
unit-specific (idiosyncratic) disturbance terms, which are assumed to be independently distributed of (dt , xit ). Since the unobserved factors ft could be correlated with (dt , xit ), a
general specification of the cross unit-specific regressors is adopted
xit = Ai dt + Γi ft + vit ,
(31)
where Ai and Γi denote (n × k) and (m × k) factor loading matrices with fixed components,
and vit are the specific components of xit distributed independently of the common effects
and across i, but assumed to follow general covariance stationary processes.
Combining Equations (29)-(31) yields the system
⎛ ⎞
⎜⎜⎜y ⎟⎟⎟
⎜ it ⎟
zit = ⎜⎜⎜⎜ ⎟⎟⎟⎟ = Bi dt + Ci
ft + uit ,
⎝ x ⎠ ((k+1)×n)(n×1) ((k+1)×m)(m×1)
((k+1)×1)
((k+1)×1)
(32)
it
where
⎛
⎞ ⎛
⎞⎛ ⎞
⎞
⎞
⎛
⎛
⎜⎜⎜ε + β v ⎟⎟⎟ ⎜⎜⎜1 β ⎟⎟⎟ ⎜⎜⎜ε ⎟⎟⎟
⎜⎜⎜ 1 0 ⎟⎟⎟
⎜⎜⎜ 1 0 ⎟⎟⎟
it ⎟
⎜
⎜
⎜⎜⎜ it
⎟
⎟
⎟⎟⎟
⎜
⎜
i it ⎟
i
⎟⎟⎟ = ⎜⎜⎜
⎟⎟⎟ ⎜⎜⎜ ⎟⎟⎟ , Bi = α A ⎜⎜⎜
⎟⎟⎟ , Ci = γ Γ ⎜⎜⎜
uit = ⎜⎜
⎟⎟ ,
i
i ⎜
i
i ⎜
⎟⎠ ⎜⎝
⎟⎠ ⎜⎝ ⎟⎠
⎟⎠
⎝ v
⎝
⎝
βi Ik
βi Ik ⎠
0 Ik vit
it
(33)
with Ik as the identity matrix of order k. The rank of Ci is determined by the rank of the
(m × (k + 1)) matrix of the unobserved factor loadings Γ̃i = γi Γi .11
Pesaran (2006) suggested the use of cross-section averages of the dependent variable, yit ,
and the regressors, xit , as proxies for the unobserved common factors. For illustration pur11
See Pesaran (2006) for details on the underlying assumptions.
21
poses of the elimination of those factors, consider the simple cross-section averages of the
Equations in (32)12
z̄t = B̄ d + C̄ ft + ūt ,
where z̄t = 1/N
N
i=1 zit ,
v̄t = 1/N
N
i=1
uit , B̄ = 1/N
N
i=1
(34)
Bi and C̄ = 1/N
N
i=1 C i .
Suppose
that Rank(C̄) = m ≤ k + 1 for all N, so that ft = (C̄C̄ )−1C̄(z̄t − B̄ dt − ūt ). If ut → 0 and
p
C̄ →
− C as N → ∞ then
p
− 0, as N → ∞.
ft − (CC )−1C(z̄t − d̄) →
(35)
This suggests that it is valid to use h̄t = (dt , z̄t ) as observable proxies for the unobservable
common factors ft , and justified the basic idea of the common correlated effects (CCE) estimators proposed by Pesaran (2006).
Pesaran (2006) presents two estimators of the means of the cross unit-specific slope coefficients. One is the mean group (MG) estimator developed in Pesaran and Smith (1995)
and the other is a generalisation of the fixed effects (FE) estimator that considers potential
cross-sectional dependence. First, the common correlated effects mean group (CCEMG)
estimator is a simple average of the individual CCE estimators, b̂i of βi , defined as
N
1
b̂i ,
N i=1
(36)
b̂i = (Xi M̄Xi )−1 Xi M̄yi ,
(37)
b̂CCEMG =
where Xi = (xi1 , ..., xiT ) , yi = (yi1 , ..., yiT ), and M̄ = IT − H̄(H̄ H̄)−1 H̄ with H̄ = (D, Z̄),
where D and Z̄ denote the (T × n) and (T × (k + 1)) matrices of observations on dt and z̄t ,
respectively.
Second, if the individual slope coefficients, βi , are the same, efficiency could be gained by
pooling. Hence, Pesaran (2006) developed the common correlated effects pooled (CCEP)
12
Pesaran (2006) applied more general weighted cross-section averages. To simplify the illustration, this
study restricts the discussion about the CCE estimators to simple averages (see Kapetanios et al., 2011).
22
estimator given by
b̂CCEP
⎞−1 N
⎛ N
⎟⎟ ⎜⎜⎜ ⎜
Xi M̄yi .
= ⎜⎝
Xi M̄Xi ⎟⎟⎟⎠
i=1
3.5
(38)
i=1
Panel Causality
To examine the direction of causality between energy consumption and economic growth
this study employs a dynamic panel error-correction specification
ΔYit = αyi +
ΔEit = αei +
h
k=1
h
k=1
y
θ1i,k
ΔYi,t−k +
e
θ1i,k
ΔEi,t−k +
h
k=0
h
y
θ2i,k
ΔEi,t−k + λyi εyi,t−1 + uyit
(39)
e
θ2i,k
ΔYi,t−k + λei εei,t−1 + ueit ,
(40)
k=0
where i = 1, ..., N represents the countries and t = 1, ..., T denotes the time period while Yit
and Eit are economic growth and energy consumption in logarithms, respectively. Δ denotes
the first-difference operator, αi stands for the fixed effects, k denotes the lag length, εi,t−1
represents the one period lagged error-correction term, and uit is the serially uncorrelated
j
j
error term with mean zero. The coefficients θ1i,k
and θ2i,k
, j = y, e, denote the short-run
dynamics while λij , j = y, e, represents the speed of adjustment. The present paper applies
the pooled mean group (PMG) estimator proposed by Pesaran et al. (1999) to estimate the
Equations (39) and (40). While instrumental variable estimators such as the widely used
Arellano and Bond (1991) GMM estimator require pooling of individuals and allow only
the intercepts to differ across countries, the PMG estimator allows for the investigation of
long-run homogeneity without making the less plausible assumption of identical short-run
dynamics in each country. Furthermore, the mean group estimator (see Pesaran and Smith,
1995) that averages the coefficient of the country-specific regressions is a consistent but no
good estimator when either N or T is small (Hsiao et al., 1999). In comparison, the PMG
estimator relies on a combination of pooling and averaging of coefficients. The optimal lag
length is selected by means of the Schwarz Information Criterion.
The direction of causality can be determined by testing for the significance of the coefficients
of each dependent variable in Equations (39) and (40). First, this study considers short23
y
e
run causality by testing the null hypotheses H0 : θ2ik
= 0 and H0 : θ2ik
= 0, ∀ik. The
former checks whether causality runs from energy consumption to economic growth and
the latter whether economic growth leads energy consumption. Second, long-run causality
can be identified by testing the significance of the speed of adjustment, i.e. to test whether
the coefficient of the respective error-correction term represented by λij , j = y, e, is equal
to zero. Finally, this study tests for strong causality by applying joint tests including the
coefficients of the respective explanatory variable and the respective error-correction term
of each equation. Since all variables are represented in stationary form the various null
hypotheses can be tested using standard Wald tests with a chi-squared distribution.
4
4.1
Empirical analysis
Data and empirical specification
This study uses annual data from 1971 to 2009 for 23 OECD countries. These are Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hungary,
Ireland, Italy, Japan, Luxembourg, Mexico, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, the United Kingdom, and the United States. Data on real GDP per capita
in constant 2000 U.S. dollars is used as a proxy for economic growth (Y) and energy consumption is represented by energy use in kilograms of oil equivalent per capita (E).13 All
variables are in natural logarithms and have been obtained from the World Bank’s World
Development Indicators.
To examine the energy consumption-growth nexus the present empirical analysis is based
on the following panel regression model specifying the relationship between real GDP per
capita, Yit , and energy consumption per capita, Eit ,
Yit = αi + βi Eit + εit ,
(41)
13
This study uses per capita data because they are less sensitive to territorial changes and provide the variables in the same units for countries of different sizes (Lanne and Liski, 2004).
24
where i = 1, ..., N represents each of the 23 OECD countries and t = 1, ..., T denotes each
year during the period 1971 to 2009.
4.2
Cross-section dependence tests
As a first step, this study applies the cross-section dependence (CD) test developed by Pesaran (2004) to verify the consideration of cross-section dependence in the analysis of the
energy consumption-growth nexus. Thus, both real GDP per capita and energy consumption
per capita are initially tested for dependence across the 23 OECD countries under investigation. The pair-wise correlations which are necessary to compute the CD statistics are
obtained from the residuals of the regression of each variable on a constant, a linear trend
and a lagged dependent variable for each country. The results of the CD tests based on these
correlations indicate that GDP and energy consumption are highly dependent across countries. The null hypothesis of cross-section independence can be clearly rejected by a value
of 43.80 for real GDP (p = 0.45) and 31.63 for energy consumption (p = 0.34).14 This
finding underlines the already mentioned importance of taking into account cross-section
dependence when analysing the energy consumption-growth nexus.
4.3
Unit root tests
As a starting point of the integration analysis, this study applies the first generation panel
unit root tests which neglect the presence of both structural breaks and cross-section dependence, but are commonly used in the panel data literature on the energy consumption-growth
nexus. Specifically, the Levin et al. (2002) (LLC) test and the t-statistic proposed by Breitung (2000) which both tests for a common unit root process as well as the W-statistic
suggested by Im et al. (2003) (IPS), the Fisher-type ADF and Fisher-type PP test (see Choi,
2001; Maddala and Wu, 1999) that assume individual unit root processes are applied. Without exception, all unit root tests assume non-stationarity under the null hypothesis. Since
these tests are meanwhile widely used and previously described the present paper does not
discuss further details of them. As displayed in Table 2, the results suggest that real GDP
14
The CD test are performed using the Stata routine "xtcsd" proposed by De Hoyos and Sarafidis (2006).
25
per capita and energy consumption per capita are integrated of order one, I(1).15
Table 2: Panel unit root test statistics without structural breaks and cross-section dependence
Variable
LLC
Breitung
IPS
ADF-Fisher
PP-Fisher
Y
ΔY
E
ΔE
3.15
-7.07∗∗∗
1.13
-18.59∗∗∗
10.53
1.09
5.33
-8.80∗∗∗
1.19
-12.05∗∗∗
-0.00
-21.84∗∗∗
47.14
237.38∗∗∗
51.85
458.26∗∗∗
24.39
192.67∗∗∗
48.41
465.91∗∗∗
Notes: Probabilities for the Fisher-type tests are computed using an asymptotic Chi-square distribution. All other tests assume
asymptotic normality. The choice of lag levels for the Breitung, IPS and Fisher-ADF test are determined by empirical realisations of the
Schwarz Information Criterion. The LLC and Fisher-PP tests were computed using the Bartlett kernel with automatic bandwidth
selection.
∗∗∗ , ∗∗
and ∗ indicate significance at the 1%, 5% and 10% levels, respectively.
The failure of the first generation panel unit root tests to reject the null of non-stationarity
for the levels of the variables may be due to the omission of structural breaks (Perron, 1989).
Thus, the consideration of structural breaks and, additionally, cross-section dependence
should provide more reliable results. Consequently, this study applies the second generation panel unit root test proposed by Bai and Carrion-i-Silvestre (2009) as a second step.
This test allows for structural breaks in the level, slope or both, which can occur at different
dates for different countries and may have different magnitudes of shift. Furthermore, the
common factor approach enables the common shocks to affect countries differently via heterogeneous factor loadings.
The results of the test developed by Bai and Carrion-i-Silvestre (2009) are presented in Table 3 and confirm the finding of non-stationarity in the variables. The null hypothesis of a
unit root cannot be rejected for all tests in the model without any break, with a break in the
mean and with a break in the trend.
4.4
Cointegration tests
Once integration of order one is established, the next step is to determine whether a long-run
relationship between GDP and energy consumption exists. To examine the existence of a
15
The results of all noted first generation panel unit root tests are examined using EViews 6.0.
26
Table 3: Panel unit root test statistics with structural breaks and cross-section dependence
Model
Test
Constant and trend
Z
P
Pm
Z
P
Pm
Z
P
Pm
Z∗
P∗
P∗m
Mean shift
Trend shift
Y
E
0.56
33.36
-1.32
0.34
38.35
-0.80
-0.20
44.37
-0.17
1.49
35.91
-1.05
-0.53
57.75
1.22
-0.75
38.51
-0.78
-1.06
49.04
0.32
1.05
45.89
-0.01
Notes: P∗ and P∗m denote the corresponding P and Pm statistics that are computed by means of the p-values of the simplified MSB
statistics, respectively. The 1%, 5% and 10% critical values for the standard normal distributed Z and Pm statistics are 2.326, 1.645 and
1.282, while the critical values for the chi-squared distributed P statistic are 71.201, 62.830 and 58.641, respectively. The number of
common factors are estimated using the panel Bayesian information criterion proposed by Bai and Ng (2002).
cointegration relationship this study repeats both types of tests, with and without structural
breaks and cross-sectional dependence. Firstly, the first generation panel cointegration tests
proposed by Kao (1999) and Pedroni (1999, 2004), and implemented in EViews 6.0, are
applied. Kao (1999)’s test is a generalisation of the Dickey-Fuller (DF) and Augmented
Dickey-Fuller (ADF) tests in the context of panel data. Pedroni proposes seven test statistics that can be distinguished in two types of residual based tests. Four tests are based on
pooling the residuals of the regression along the within-dimension of the panel (panel tests),
while three are based on pooling the residuals along the between-dimension (group tests).
Both Kao and Pedroni assume the null hypothesis of no cointegration and use the residuals
determined by a panel regression to construct the test statistics and determine the asymptotically normal distribution.
Table 4 reports the empirical realisations of Kao’s and Pedroni’s panel cointegration tests.
With the exception of the panel υ-statistic in the case with trend, none of the test statistics
result in the rejection of the null hypothesis of no cointegration. Hence, the results of these
first generation panel cointegration tests that neither allow for structural breaks nor cross-
27
section dependence suggest no evidence for a long-run equilibrium relationship between
energy consumption per capita and real GDP per capita.
Table 4: Panel cointegration test results without structural breaks and cross-section dependence
Pedroni’s panel cointegration test results
without trend
Test statistics
with trend
Values
Panel υ-Statistic
Panel ρ-Statistic
Panel PP-Statistic
Panel ADF-Statistic
Group ρ-Statistic
Group PP-Statistic
Group ADF-Statistic
Test statistics
Panel υ-Statistic
Panel ρ-Statistic
Panel PP-Statistic
Panel ADF-Statistic
Group ρ-Statistic
Group PP-Statistic
Group ADF-Statistic
-2.60
2.24
2.32
2.25
1.51
2.05
1.28
Values
15.96∗∗∗
2.55
2.05
2.03
2.38
1.71
1.11
Kao’s panel cointegration test result
ADF-statistic
-1.10
Notes: The null hypothesis is that the variables are not cointegrated. Under the null hypothesis, all the statistics are distributed as
standard normal distributions. The finite sample distribution for the seven statistics has been tabulated in Pedroni (2004). *, **, and ***
indicate that the estimated parameters are significant at the 10%, 5%, and 1% levels, respectively.
Similar to the first generation unit root tests, the first generation panel cointegration tests
may not be able to reject the null because of the missing consideration of structural breaks.
Hence, in a second step, this study applies the LM-based tests proposed by Westerlund
and Edgerton (2008) that simultaneously consider cross-section dependence and structural
breaks, which may be located at different dates for different panel members. Additionally,
this test allows for heteroskedastic and serially correlated errors, and cross unit-specific time
trends.
Both test statistics Zφ (N) and Zτ (N) of Westerlund and Edgerton (2008) reveal evidence in
favour of a long-run relationship between energy consumption per capita and real GDP per
capita when allowing for breaks in the level and the slope of this relationship (see Table
5). Narayan and Smyth (2008) proposed the same finding that Pedroni’s test statistics do
not reject the null of no cointegration whereas once structural breaks are incorporated they
found cointegration by means of the test suggested by Westerlund (2006).
28
Table 5: Panel cointegration test results with structural breaks and cross-section dependence
Model
Zφ (N)
Zτ (N)
No break
Mean shift
Regime shift
-5.33∗∗∗
-1.68∗∗∗
-1.48∗
-1.75∗∗∗
-2.27∗∗
-2.41∗∗∗
Notes: The LM-based test statistics Zφ (N) and Zτ (N) are normal distributed. The number of common factors is determined by means of
the information criterion proposed by Bai and Ng (2004) and the maximum number is set to 5. *, **, and *** indicate significance at the
10%, 5%, and 1% levels, respectively.
Furthermore, Table 6 reports the contemporaneously estimated breaks for each country. Applying the approach of Westerlund and Edgerton (2008) this study finds one structural break
for each country in both specifications with mean shift and regime shift. Those can be associated with huge global shocks. Several countries share the common break dates 1974 in
consequence of the first oil crisis in 1973, 1990 at the time of Iraq’s invasion of Kuwait with
the subsequent oil price increase, 2002 in the aftermath of the sharp oil price decreases in
the 1997-1999 Asian crisis and in 2001/2002 around the September 11 attacks, and 2005
marking the large and continued rise in oil prices until 2008. Additionally, there are many
occasional breaks in the late 1970s and during the 1980s reflecting the turbulence throughout this period including the 1978 Iranian revolution and the Iran-Iraq War, accompanied
by exploding oil prices and a period of high inflation during the late 1970s, the global economic recession in the early 1980s, the fall in oil prices in 1986, the 1987 Wall Street stock
market crash, and the periods of moderate economic growth and low inflation in Western
industrialised countries in the late 1980s and early 1990s.
A comparison with previous studies reporting explicit estimated break dates in the cointegration relation between energy consumption and economic growth reveals that these findings
can be roughly confirmed by Narayan and Smyth (2008) who found structural breaks of the
energy consumption-growth nexus for the G7 countries during the 1980-1988 sub-period of
the whole sample period 1972-2002, and Lee and Chiu (2011) who provide the occurrence
of structural breaks for six developing countries during the periods 1976-1979, 1982-985,
and 1991-1992 when analysing nuclear energy consumption from 1971-2006. Since the
29
Table 6: Estimates of breaks
Country
Mean shift
Regime shift
1982
1976
1979
1990
1974
1979
1992
1990
1986
1990
1978
2002
1984
1985
1999
1998
2002
1974
1977
1992
1974
1990
1990
1982
2005
1979
1990
2005
1979
1976
2002
1986
1990
1987
2002
1998
1985
1999
2005
1988
1974
1986
2005
1974
1990
1990
Australia
Austria
Belgium
Canada
Denmark
Finland
France
Germany
Greece
Hungary
Ireland
Italy
Japan
Luxembourg
Mexico
Netherlands
Norway
Portugal
Spain
Sweden
Switzerland
United Kingdom
United States
Notes: The break dates are selected by means of the test approach suggested in Westerlund and Edgerton (2008) which follows the
strategy of Bai and Perron (1998) to determine the location of structural breaks.
30
present analysis includes three to four times more countries than the studies by Narayan and
Smyth (2008) and Lee and Chiu (2011) over a larger sample period, this paper is able to
more clearly determine structural breaks that are common to several countries due to global
shocks such as the first oil crisis in 1973.
4.5
Long-run estimations
As a next step, the present paper explicitly estimates the long-run relationships between
energy consumption per capita and real GDP per capita:
Yi,t = αyi + δyi t + βyi Ei,t + εyi,t
Ei,t = αei + δei t + βei Yi,t + εei,t
(42)
where i = 1, ..., N refers to each country in the panel and t = 1, ..., T denotes the time period,
αi and δi are country-specific fixed effects and time trends, respectively. For this purpose,
this study uses not only the fixed effects (FE) and mean group (MG) estimator proposed by
Pesaran and Smith (1995) but also Pesaran’s (2006) common correlated effects (CCE) estimators to consider the presence of common factors which cause cross-section dependence.
In addition to dependence across countries, the detected structural breaks can be taken into
account by including country-specific dummy variables that are specified accordingly to the
estimated break dates (see Table 6) as described in the robustness check below.
The results of the long-run estimates are reported in Table 7. The first two columns give the
naive pooled fixed effects and mean group estimates. As the CD test statistics show, these
exhibit considerable cross-section dependence. In contrast, the common correlated effects
pooled (CCEP) and common correlated effects mean group (CCEMG) estimates in the other
two columns have a purged and, hence, greatly reduced cross-section dependence. The estimated income elasticities of energy consumption, βe , in the first row of Table 7 (0.50-0.71)
are larger than the estimated long-run coefficients of energy consumption, βy , affecting real
GDP (0.26-0.41). This finding indicates, regardless of the yet to be determined direction of
causation, that real GDP has a stronger impact on energy consumption in the long run than
31
vice versa.
The same conclusion might be drawn from other empirical studies analysing the energy
consumption-growth nexus for OECD countries that report estimated long-run elasticities.
Lee et al. (2008) estimated a long-run coefficient of energy consumption of 0.25 and Narayan
and Smyth (2008) reported the corresponding values 0.12, 0.16 and 0.39 whereas Lee and
Lee (2010) estimated a larger value for the income elasticity of 0.52. However, as long as
there are only a few studies reporting long-run elasticities no conclusion can be drawn. A
comparison of these results with those of the present study reveals that they do not differ to
an important degree. The reported values of previous studies are slightly smaller, if different
at all, which might be due to the inclusion of either energy prices or capital as an additional
explanatory variable.
Table 7: Results of long-run estimations
Dep.
FE
MG
CCEP
CCEMG
Var.
β
CD
β
CD
β
CD
β
CD
Yit
0.41 [7.95]
12.95
0.40 [8.06]
14.37
0.40 [4.81]
-3.76
0.26 [3.65]
-3.50
Eit
(0.05)
0.64 [5.75]
(0.11)
22.61
(0.05)
0.71 [8.05]
(0.09)
19.62
(0.08)
0.66 [4.21]
(0.16)
-4.01
(0.07)
0.50 [3.91]
(0.13)
-3.69
Notes: Numbers in parentheses are standard errors and numbers in brackets represent the t-statistics. CD denotes the cross-section
dependence test proposed by Pesaran (2004) which assumes cross-section independence under the null hypothesis.
Furthermore, the present paper checks the robustness of its estimated long-run elasticities
by the inclusion of country-specific dummy variables that are specified according to the detected breaks in the mean and/or trend as reported in Table 6 and oil prices as an observed
common factor. The results do not qualitatively change and are available upon request from
the author.
4.6
Dynamic panel causality
Finally, this section analyses the main objective of this study on the energy consumptiongrowth nexus: the direction of causation between energy consumption and economic growth.
This is done by the application of the pooled mean group (PMG) estimator proposed by Pe32
saran et al. (1999) to the dynamic panel error-correction specification in Equations (39) and
(40), and Wald chi-squared tests to evaluate the various Granger causality relationships.16
Table 8 shows the corresponding results.
Table 8: Results of panel causality tests for the energy consumption-growth nexus in OECD
countries - revisited
Dependent
Variable
Sources of causation (independent variable)
Short-run
ΔY
ΔE
ΔY
235.87∗∗∗
(0.80)
ΔE
74.69∗∗∗
-
(0.24)
Long-run
Strong causality
ECT
-0.06∗∗∗
-0.11∗∗∗
ΔY, ECT
238.22∗∗∗
ΔE, ECT
154.46∗∗∗
-
Notes: Table 8 reports the empirical realisations of the Wald chi-squared test statistics for short-run and strong causality. The sum of the
(lagged) coefficients for the respective short-run changes is denoted in parentheses. The lag length is two. ECT represents the coefficient
of the error-correction terms εy and εe , respectively.
∗∗∗ , ∗∗
and ∗ indicate that the null hypothesis of no causation is rejected at the 1%,
5% and 10% levels, respectively.
The empirical exercise reveals a bi-directional causal relationship between ΔY and ΔE in all
three cases, short-run, long-run and strong causality. Hence, energy consumption per capita
Granger-causes real GDP per capita and vice versa, implying that an increase in one leads
to an increase in the other. Similar to the long-run estimation results, the examination of
the sum of lagged coefficients on the respective variable indicates that real GDP (0.80) has
also in the short run a greater impact on energy consumption than vice versa (0.24). Furthermore, the significance of the error correction terms (ECT) indicates that both variables
readjust towards a long-run equilibrium relationship after a shock occurs. The estimated
speed of adjustment of real GDP (-0.06) is slightly slower than the speed of adjustment of
energy consumption (-0.11). With respect to the energy consumption-growth nexus these
findings lend support for the feedback hypothesis which argues that energy consumption
and real GDP affect each other simultaneously.
In the empirical literature on the energy consumption-growth nexus of OECD countries the
16
This study uses the Stata routine "xtpmg" proposed by Blackburne and Frank (2007) to estimate the
dynamic panel error-correction model by means of the pooled mean group estimator and test for significance.
33
same finding is also reported by the panel data analyses of Lee and Chang (2007), Lee et al.
(2008), Costantini and Martini (2010), Lee and Lee (2010), and Belke et al. (2011). More
precisely, Costantini and Martini (2010) and Lee and Lee (2010) report bi-directional shortrun and strong causality whereas in the long run real GDP is found to be a driver for energy
consumption indicating that energy policies have no adverse impact on economy’s long-run
growth. The smaller long-run and adjustment coefficients of energy consumption compared
to real GDP estimated by the present study also give evidence in this direction. Compared
with other previous panel data studies on OECD countries, the findings of bi-directional
causal relationships contradict, on the one hand, those of Huang et al. (2008) who found a
uni-directional causal relationship running from economic growth to energy consumption
with a negative impact, and, on the other, those of the panel data analysis by Narayan and
Smyth (2008) who inferred that energy consumption Granger-causes real GDP positively
in the long run. Furthermore, the empirical results of this study also refute the neutrality
hypothesis such as all other panel data studies on the energy consumption-growth nexus,
except for the sub-analysis by Huang et al. (2008) of 19 low income countries.
5
Conclusion
This study has analysed the causal relationship between real GDP and energy consumption
for a panel of 23 OECD countries covering the period 1971-2009. Recognising the lack
consensus of the widely studied energy consumption-GDP growth nexus it is appropriate to
take into special consideration important issues that were largely neglected by the empirical
literature so far. These include most of all structural breaks and dependence across countries
when using panel data. Their consideration is promising toward providing more suitable and
reliable results since the occurrence of critical energy and economic events that likely may
cause structural breaks and the existence of strong inter-economic linkages between OECD
countries cannot plausibly be ignored. Consequently, the present paper has applied recently
developed panel econometric techniques to tackle these issues.
Indeed, a long-run equilibrium relationship between real GDP and energy consumption can
34
only be found when taking into account structural breaks and cross-section dependence. In
addition, the thereby estimated breaks can be associated with well-known global shocks.
The empirical evidence reveals that a 1% increase in energy consumption leads to an increase in real GDP of 0.26-0.41%. In turn, the estimated income elasticity of energy consumption turns out to be 0.50-0.71. Furthermore, panel causality tests indicate bi-directional
causality between real GDP and energy consumption in the short and long run. Hence, no
variable leads the other. This finding supports evidence for the feedback hypothesis which
argues that real GDP and energy consumption affect each other simultaneously.
Strong policy implications emerge for governments with regard to the implementation of
energy conservation policies. Initially, the empirical results suggest that energy consumption and real GDP are both endogenous and, hence, single equation forecasts of one of them
might be misleading. Furthermore, energy conservation policies, on the one hand, are faced
with the unpleasant situation of directly and adversely affecting economic growth when reducing energy consumption. On the other hand, there may also be an indirect feedback
effect of economic growth on energy consumption. Interestingly, the empirical results suggest that in the short and long run, energy consumption has a smaller impact on economic
growth than vice versa. Thus, the adverse affect of energy conservation policies on economic
growth should not be overemphasized as compared to the larger impact of economic growth
on energy consumption. However, policy makers may be worried about limiting economic
growth even though the OECD countries have high potential for energy savings since their
level of energy consumption per capita and CO2 emissions per capita are far above the world
averages. Hence, to ease the trade-off between energy consumption and economic growth
such governments should implement energy policies that emphasise the use of alternative
energy sources rather than exclusively try to reduce overall energy consumption in order
to minimise dioxide emissions. Accordingly, they should make the necessary efforts to increase the investments in energy infrastructure and the restructuring of the energy sector to
change the composition of energy consumption by substituting environmental friendly energy sources for fossil fuels (see Lee and Lee, 2010; Narayan and Smyth, 2008). To reduce
greenhouse gas emissions OECD countries should also encourage their industries to invest
35
in new technologies that make alternative energy sources more feasible.
However, the empirical finding that energy consumption causes economic growth does not
necessarily imply that energy conservation will harm economic growth if energy-efficient
production technologies are used. In fact, a reduction in energy consumption due to improvements in energy efficiency may raise productivity, which in turn may stimulate economic growth. Thus, a shift from less efficient and more polluting energy sources to more
efficient energy options may establish a stimulus rather than an obstacle to economic development (Costantini and Martini, 2010).
Moreover, the empirical results of the present study indicate that there is cross-section dependence in real GDP, energy consumption and their long-run relationship, and that such a
relation can only be detected when considering structural breaks. These findings suggest the
importance for policy makers to base their decisions on studies of the long-run relationship
and direction of causation that take into account relationships of dependency across countries and the impact of past exogenous shocks. Hence, this study motivates both researchers
and politicians to follow this new direction of research to properly assess energy models,
reliably predict future developments, and design sensible energy policies to restructure the
energy sector and conserve energy. An interesting task for future research may be the analysis of supplementary energy sources and different sectoral patterns of energy consumption
for a sensible implementation of specific energy policies.
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